The strategy of constraining the lepton flavor mixing from remnant CP symmetry is investigated in a rather general way. The neutrino mass matrix generally admits four remnant CP transformations which can be derived from the measured lepton mixing matrix in the charged lepton diagonal basis. Conversely, the lepton mixing matrix can be reconstructed from the postulated remnant CP transformations. All mixing angles and C\P-violating phases can be completely determined by the full set of remnant CP trans formations or three of them. When one or two remnant CP transformations are preserved, the resulting lepton mixing matrix would depend on three real parameters or one real parameter, respectively, in addition to the parameters characterizing the remnant CP. The concrete form of the mixing matrix is also presented. The phenomenological predictions for the mixing parameters are discussed. The conditions leading to vanishing or maximal Dirac CP violation are studied.

We study lepton mixing patterns which can be derived from the A 5 family symmetry and generalized CP. We find five phenomenologically interesting mixing patterns for which one column of the PMNS matrix is () T (the first column of the golden ratio mixing), () T (the second column of the golden ratio mixing), (1, 1, 1) T / √ 3 or ( √ 5 + 1, −2, √ 5 − 1) T /4. The three lepton mixing angles are determined in terms of a single real parameter θ, and agreement with experimental data can be achieved for certain values of θ. The Dirac CP violating phase is predicted to be trivial or maximal while Majorana phases are trivial. We construct a supersymmetric model based on A 5 family symmetry and generalized CP. The lepton mixing is exactly the golden ratio pattern at leading order, and the mixing patterns of case III and case IV are reproduced after higher order corrections are considered.

We discussed the scenario that a discrete flavor group combined with CP symmetry is broken to Z 2 × CP in both neutrino and charged lepton sectors. All lepton mixing angles and CP violation phases are predicted to depend on two free parameters θ l and θ ν varying in the range of [0, π). As an example, we comprehensively study the lepton mixing patterns which can be derived from the flavor group ∆(6n 2 ) and CP symmetry. Three kinds of phenomenologically viable lepton mixing matrices are obtained up to row and column permutations. We further extend this approach to the quark sector. The precisely measured quark mixing angles and CP invariant can be accommodated for certain values of the free parameters θ u and θ d . A simultaneous description of quark and lepton flavor mixing structures can be achieved from a common flavor group ∆(6n 2 ) and CP, and accordingly the smallest value of the group index n is n = 7.

The lepton flavor mixing matrix having one row or one column in common with the bimaximal mixing up to permutations is still compatible with the present neutrino oscillation data. We provide a thorough exploration of generating such a mixing matrix from S 4 family symmetry and generalized CP symmetry H CP . Supposing that S 4 H CP is broken down to Z ST 2 SU 2 × H ν CP in the neutrino sector and Z T ST 2 U 4H l CP in the charged lepton sector, one column of the PMNS matrix would be of the form 1/2, 1/ √ 2, 1/2 T up to permutations, both Dirac CP phase and Majorana CP phases are trivial to accommodate the observed lepton mixing angles. The phenomenological implications of the remnant symmetry K× H ν CP in the neutrino sector and Z SU 2 × H l CP in the charged lepton sector are studied. One row of PMNS matrix is determined to be 1/2, 1/2, −i/ √ 2 , and all the three leptonic CP phases can only be trivial to fit the measured values of the mixing angles. Two models based on S 4 family symmetry and generalized CP are constructed to implement these model independent predictions enforced by remnant symmetry. The correct mass hierarchy among the charged leptons is achieved. The vacuum alignment and higher order corrections are discussed.

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